Today We will: Create linear equations from a context and model with tables and graphs.
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1 U2D11 Math 8C U2D11 Today We will: Create linear equations from a context and model with tables and graphs.
2 U2D11 A quick review: Plotting Points Plot the points A(2, 3) B(-1, -4) C(-3, 3) C A D(4, -2) D B
3 U2D11 Plotting Points Write the ordered pair that corresponds to point B. Now do the same for points A, C, & D (-3,4) (-2, 1) (-4, -3) (1, -2) (5, 4) (3, -4)
4 Example There are $500 in Holly s bank account. Every month she takes $50 out, but does not make any deposits. Make a table of values. Make a graph. Write an equation. U2D11 Equation:
5 Example A rental car company charges an initial fee $50 and then $0.20 for each mile it is driven. 1 st, make a table of values and a graph to represent total cost. 2 nd, write an equation to represent total cost C, in terms of miles, m U2D11 Miles Cost Equation:
6 You Try! Lin is tracking the progress of her plant s growth. Today the plant is 5 cm high and she knows that plant will continue to grow 1.5 cm each day. Make a table of values for 0-5 days. Make a graph (don t forget to label your axes and scale!) Write an equation that represents the plant s growth per day. U2D11
7 U2D11 You Try!! A taxi ride has a flat fee of $3.50 and a charge of $1.50 for every mile travelled. a) Write an equation to represent the total cost b) How much would you expect to pay for a trip of 15 miles?
8 Independent Practice U2D11 U2D11 ICP Due Today! Also, please get me your requests to reassess ASAP as the term ends in three weeks!
9 U2D12 Math 8C U2D12 Today We will: Compute Slope
10 U2D12 What did you notice about On yesterday s practice: What did you notice about where the line crossed the y-axis? What did you notice about the steepness of the line and one of the numbers in your equation? What did you notice about the shape of each line? Straight? Curved? Crooked?
11 U2D12 Linear Equations A linear equation is an equation whose graph is a straight line. Every point on the line is a solution of the equation. These equations can be written in the form y mx b where m is the slope of the line, and b is the y-intercept of the line.
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13 U2D12 Example From yesterday: The equation that represented Paulina s bank account savings was S 150m 350 What is the slope of the line? What is the y-intercept? slope 150 y intercept 350 What do these values represent for Paulina?
14 U2D12 What is slope? Slope is a rate of change. Slope is the steepness of a line. How do we measure slope? How steep is this line?
15 U2D12 Slope Formula rise run 4 3 slope change iny change inx rise run
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17 U2D12 Find the slope of each line Slope of line a= 1 2 Slope of line b= - 2 Slope of line c= 0 Slope of line d= 2 0 undefined
18 U2D12 If given only two points on a line We know that slope is change iny change inx So, if given (-2,4) and (4, 12), find the change in y and in x. Slope = change iny change inx
19 U2D12 Formula! If given two points (x1,y1 ) and (x2,y2 ) slope y x 2 2 y x 1 1
20 U2D12 Example Find the slope of the line crossing through each pair of points: (8, 10), (3, 20) (-2, 4), (9, -7) (6, -2), (6, 11) (5, -1), (1, -1)
21 Independent Practice U2D12 - ICP
22 U2D13 Math 8C U2D13 Today We will: Create linear equations from a context and model with tables and graphs. Compare linear equations of the form y = mx with equations of the form y = mx + b. Compare and contract linear functions represented differently.
23 U2D13 Warm Up Sudzo Wash and Wax charges customers $0.75 per minute to wash a car. Write an equation that relates the total charge C to the amount of time t in minutes.
24 Practice U2D13 What does this graph show? Write the equation of the line shown on the graph.
25 U2D13 Graphing Lines What do we need to know about a line in order to graph it? Slope A point on the line
26 U2D13 Equations in Slope-Intercept Form When equations are in Slope-Intercept form, we have the slope and a point! The y-intercept is a point on the y-axis, with ordered pair (0, b)
27 U2D13 Equations in Slope-Intercept Form When equations are in Slope-Intercept form, we are given the slope and a point on the y- axis. Example Graph y = 3x + 2 Slope y-intercept
28 U2D13 Equations in Slope-Intercept Form Where do we start when graphing a line? Example Graph y = 3x + 2 Slope y-intercept 1 st plot the y-intercept 2 nd use slope to find a second point. rise = +3 run +1 Last, connect dots to draw the line
29 U2D13 Graph Each Line y = 2x 2 y = x + 1 y = 2 5 x + 3 y = 1 3 x 1
30 Warm Up U2D13 Marty is spending money at the average rate of $3 per day. After 14 days he has $68 left. The amount left depends on the number of days that have passed. Identify the variables in this situation: x= y= What is the given information in this problem (find all that apply)? y-intercept slope one point (, ) second point (, ) a) What amount of money did he begin with? b) Write an equation for the situation.
31 U2D13 Find the slope 1. (2, 1), (3, 6) (-2, -2), (-7, -7) 3. (2, 1), (2, -7) 5.
32 U2D13 Graph Each Line y = 3x 1 y = x y = 4 5 x 3 y =
33 U2D13 What about these weird ones? How would you graph something like y = 2? This equation says that y can only ever be 2, regardless of what x is. How about something like x = 3? This equation says that x can only ever be -3, no matter what y is.
34 Graph y = 2 U2D13
35 Graph x = 3 U2D13
36 U2D13 You Try! State the slope and the y-intercept of each line. Then graph the line of each equation: 1. y = 2x 3 2. y = 1 3. y = 3 4 x x = 5
37 Independent Practice U2D13 ICP Heads Up! Quiz on Monday(FA) There will be a Summative Assessment on D11-D14 next week.
38 U2D14 Math 8C U2D14 Today s Quiz: Construct viable arguments and critique the reasoning of others. Interpret the results of mathematics in terms of the context in which it was presented. Create linear equations from a context and model with tables and graphs. Compare linear equations of the form y = mx with equations of the form y = mx + b. Compute slope.
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